8/6/2018
Indian Institute of Technology Jodhpur, Year 2018 Analog Electronics (Course Code: EE314) Lecture 2: Introduction & Semiconductor Basics
Course Instructor: Shree Prakash Tiwari Email: [email protected]
Webpage: http://home.iitj.ac.in/~sptiwari/
Note: The information provided in the slides are taken form text books for microelectronics (including Sedra & Smith, B. Razavi), and various other resources from internet, for teaching/academic use only 1
Dopant Compensation
• An N‐type semiconductor can be converted into P‐ type material by counter‐doping it with acceptors
such that NA > ND. • A compensated semiconductor material has both acceptors and donors. N‐type material P‐type material
(ND > NA) (NA > ND)
n N D N A p N A N D n 2 n 2 p i n i N D N A N A N D
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Carrier Drift
• The process in which charged particles move because of an electric field is called drift. • Charged particles within a semiconductor move with an average velocity proportional to the electric field. – The proportionality constant is the carrier mobility. Hole velocity vh p E
Electron velocity ve n E
Notation: 2 p hole mobility (cm /V∙s) 2 n electron mobility (cm /V∙s)
Velocity Saturation
• In reality, carrier velocities saturate at an upper limit, called the saturation velocity (vsat).
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Drift Current • Drift current is proportional to the carrier velocity and carrier concentration:
vh tA= volume from which all holes cross plane in time t p vh t A = # of holes crossing plane in time t q p vh t A = charge crossing plane in time t qpvh A = charge crossing plane per unit time = hole current
Hole current per unit area (i.e. current density) Jp,drift = qpvh
Conductivity and Resistivity
• In a semiconductor, both electrons and holes conduct current:
J p,drift qp p E J n,drift qn(n E)
Jtot,drift J p,drift J n,drift qp p E qnn E
Jtot,drift q( p p nn )E E
• The conductivity of a semiconductor is qp p qnn – Unit: mho/cm 1 • The resistivity of a semiconductor is – Unit: ohm‐cm
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Resistivity Example
• Estimate the resistivity of a Si sample doped with phosphorus to a concentration of 1015 cm‐3 and boron to a concentration of 1017 cm‐3. The electron mobility and hole mobility are 800 cm2/Vs and 300 cm2/Vs, respectively.
~0.2 Ohm‐cm
Electrical Resistance V I _ +
W t homogeneously doped sample
L V L Resistance R (Unit: ohms) I Wt where is the resistivity
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Carrier Diffusion
• Due to thermally induced random motion, mobile particles tend to move from a region of high concentration to a region of low concentration. – Analogy: ink droplet in water • Current flow due to mobile charge diffusion is proportional to the carrier concentration gradient. – The proportionality constant is the diffusion constant. dp J qD p p dx Notation: 2 Dp hole diffusion constant (cm /s) 2 Dn electron diffusion constant (cm /s)
Diffusion Examples
• Linear concentration profile • Non-linear concentration profile constant diffusion current varying diffusion current x x p N1 p N exp L Ld
dp dp J qD J qD p,diff p dx p,diff p dx
N qDp N x qDp exp L Ld Ld
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Diffusion Current
• Diffusion current within a semiconductor consists of hole and electron components: dp dn J qD J qD p,diff p dx n,diff n dx dn dp J q(D D ) tot,diff n dx p dx • The total current flowing in a semiconductor is the sum of drift current and diffusion current:
Jtot J p,drift J n,drift J p,diff J n,diff
The Einstein Relation
• The characteristic constants for drift and diffusion are related: D kT q
kT • Note that 26 mV at room temperature (300K) q – This is often referred to as the “thermal voltage”.
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The PN Junction Diode
• When a P‐type semiconductor region and an N‐type semiconductor region are in contact, a PN junction dddiode is fdformed. VD – +
ID
Diode Operating Regions
• In order to understand the operation of a diode, it is necessary to study its behavior in three operation regions: equilblibrium, reverse bias, and fdforward bias.
VD = 0 VD < 0 VD > 0
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Next
• Diode contd…
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